# Integrating Using Arctan

1. Feb 1, 2009

### jumbogala

1. The problem statement, all variables and given/known data
Integrate
1/(x2 +11x +29)

2. Relevant equations

3. The attempt at a solution
I'm doing something wrong, but can't figure out what...

Complete the square so that the denominator equals (x+2)2+25

Then divide by 25: ((x+2)2)/25 + 1

Move that 25 into the squared part: ((x+2)/5)2+1

Substitute the squared part for u.

Find du/dx = 1/5, and therefore 5du=dx

Now we have 5*(integral sign) du / (u2+1)

This gives 5arctan(u)+C --> substitute u back for what you had before.

But the answer is 1/5arctan(u). Where did I go wrong?

Last edited: Feb 1, 2009
2. Feb 1, 2009

### NoMoreExams

When you "divide by 25", where does that 25 go?

3. Feb 1, 2009

### jumbogala

Oops, I was focusing so much on the denominator, I forgot about the numerator. This is what happens when yiou do math late at night, haha.

Thanks!

4. Feb 1, 2009

### Dick

You can't just divide by something and expect the answer to be unchanged. Once you have 1/((x+5)^2+25) why not just substitute (x+5)=5*u?

5. Feb 2, 2009

### djeitnstine

how about x+2 = 5tanu to make life easier